A shipping box for a refrigerator is shaped like a rectangular prism. The box has a depth of 34,25 Inches (in.), a height of 69,37 in., and a width of 32.62 in. To the nearest hundredth cubic inch, what is the volume of the shipping box?
- A. 2,262.85
- B. 77,502.59
- C. 136.24
- D. 25,834.20
Correct Answer & Rationale
Correct Answer: B
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
Other Related Questions
Ricardo has two bank accounts. Each month, he will withdraw a certain amount of money from the first account and deposit a different amount of money into the second account. The inequality 8,000 – 200x ? 5,000 + 300x can be solved to find the number of months, x, for which the account has more money than the second account. What is the solution to this inequality?
- A. x ? 6
- B. x ? 30
- C. x ? 30
- D. x ? 6
Correct Answer & Rationale
Correct Answer: D
To solve the inequality \( 8,000 - 200x > 5,000 + 300x \), we first isolate \( x \). Rearranging gives \( 8,000 - 5,000 > 300x + 200x \), simplifying to \( 3,000 > 500x \). Dividing by 500 results in \( x < 6 \). Thus, the solution indicates that for \( x \) to ensure the first account has more money, it must be less than 6 months. Option A incorrectly states \( x \geq 6 \), which contradicts the solution. Options B and C mistakenly suggest \( x \geq 30 \), which is not relevant to the problem.
To solve the inequality \( 8,000 - 200x > 5,000 + 300x \), we first isolate \( x \). Rearranging gives \( 8,000 - 5,000 > 300x + 200x \), simplifying to \( 3,000 > 500x \). Dividing by 500 results in \( x < 6 \). Thus, the solution indicates that for \( x \) to ensure the first account has more money, it must be less than 6 months. Option A incorrectly states \( x \geq 6 \), which contradicts the solution. Options B and C mistakenly suggest \( x \geq 30 \), which is not relevant to the problem.
Laura walks every evening on the edges of a sports field near her house. The field is in the shape of a rectangle 300 feet (ft) long and 200 ft wide, so 1 lap on the edges of the field is 1,000 ft. She enters through a gate at point G, located exactly halfway along the length of the field.
Laura counts the number of strides she takes during her daily walks. She takes about 80 strides to walk the width of the field from Z to W. Assuming that her stride length does not change, about how many strides does Laura take to walk all the way around the edge of the field?
- A. 267
- B. 320
- C. 450
- D. 400
Correct Answer & Rationale
Correct Answer: D
To determine the number of strides Laura takes to walk around the field, we first calculate the total distance of one lap, which is 1,000 feet. Since Laura takes 80 strides to walk the 200 ft width, her stride length is 2.5 ft (200 ft ÷ 80 strides). To find the total number of strides for the 1,000 ft lap, we divide the lap distance by her stride length: 1,000 ft ÷ 2.5 ft/stride = 400 strides. Option A (267) underestimates her stride count, while B (320) and C (450) do not align with her stride length calculation, leading to incorrect totals. Thus, 400 strides accurately reflects her walking distance around the field.
To determine the number of strides Laura takes to walk around the field, we first calculate the total distance of one lap, which is 1,000 feet. Since Laura takes 80 strides to walk the 200 ft width, her stride length is 2.5 ft (200 ft ÷ 80 strides). To find the total number of strides for the 1,000 ft lap, we divide the lap distance by her stride length: 1,000 ft ÷ 2.5 ft/stride = 400 strides. Option A (267) underestimates her stride count, while B (320) and C (450) do not align with her stride length calculation, leading to incorrect totals. Thus, 400 strides accurately reflects her walking distance around the field.
Tina Is designing a cabin. One of her plans for the cabin is a rectangle twice as long as it is wide, with 10 feet (ft) of the length reserved for the Kitchen and the bathroom. The diagram shows this basic plan. Tina wants the area of the main room to be 300 square feet. Which equation can be used to find x, the width, in feet, of the main room?
- A. 2x^2 + 10x - 300 = 0
- B. 2x^2 - 10x - 300 = 0
- C. 2x^2 - 20x - 300 = 0
- D. 2x^2 + 20x - 300 = 0
Correct Answer & Rationale
Correct Answer: B
To determine the width \( x \) of the main room, we start with the area formula for a rectangle: Area = Length × Width. The cabin's length is twice the width, so it can be expressed as \( 2x \). Since 10 ft is allocated for the kitchen and bathroom, the length of the main room is \( 2x - 10 \). The equation for the area of the main room is therefore \( (2x - 10)x = 300 \), which simplifies to \( 2x^2 - 10x - 300 = 0 \), matching option B. Option A incorrectly adds \( 10x \) instead of subtracting, leading to an incorrect area calculation. Option C miscalculates the length by subtracting 20 instead of 10, while option D incorrectly adds 20, which does not reflect the reserved space. Thus, only option B accurately represents the relationship between length, width, and area.
To determine the width \( x \) of the main room, we start with the area formula for a rectangle: Area = Length × Width. The cabin's length is twice the width, so it can be expressed as \( 2x \). Since 10 ft is allocated for the kitchen and bathroom, the length of the main room is \( 2x - 10 \). The equation for the area of the main room is therefore \( (2x - 10)x = 300 \), which simplifies to \( 2x^2 - 10x - 300 = 0 \), matching option B. Option A incorrectly adds \( 10x \) instead of subtracting, leading to an incorrect area calculation. Option C miscalculates the length by subtracting 20 instead of 10, while option D incorrectly adds 20, which does not reflect the reserved space. Thus, only option B accurately represents the relationship between length, width, and area.
Kelly has a home business making jewellery. It takes 2 hours for her to make each bracelet and 3.5 hours to make each necklace. Next month she plans to spend 140 hours to make jewellery. If she fills a special order for 22 bracelets at the beginning of the mouth and spends the rest of the month making necklaces, how many necklaces can Kelly make in the month
- A. 52
- B. 27
- C. 40
- D. 31
Correct Answer & Rationale
Correct Answer: B
To determine how many necklaces Kelly can make, first calculate the time spent on bracelets. Making 22 bracelets takes 22 x 2 = 44 hours. Subtracting this from her total available time of 140 hours leaves her with 140 - 44 = 96 hours for necklaces. Each necklace takes 3.5 hours, so she can make 96 ÷ 3.5 = 27.43, which rounds down to 27 necklaces since she cannot make a fraction of a necklace. Options A (52), C (40), and D (31) are incorrect because they exceed the available time after accounting for the hours spent on bracelets, indicating miscalculations in time management or misunderstanding of the problem constraints.
To determine how many necklaces Kelly can make, first calculate the time spent on bracelets. Making 22 bracelets takes 22 x 2 = 44 hours. Subtracting this from her total available time of 140 hours leaves her with 140 - 44 = 96 hours for necklaces. Each necklace takes 3.5 hours, so she can make 96 ÷ 3.5 = 27.43, which rounds down to 27 necklaces since she cannot make a fraction of a necklace. Options A (52), C (40), and D (31) are incorrect because they exceed the available time after accounting for the hours spent on bracelets, indicating miscalculations in time management or misunderstanding of the problem constraints.